Gradient Index Lens Research Articles

Spatial Photo-Patterning of Nematic Liquid Crystal Pretilt and its Application in Fabricating Flat Gradient-Index Lenses.

Liquid crystals offer a dynamic platform for developing advanced photonics and soft actuation systems due to their unique and facile tunability and reconfigurability. Achieving precise spatial patterning of the liquid crystal alignment is critical to developing electro-optical devices, programmable origami, directed colloidal assembly, and controlling active matter. Here, a simple method is demonstrated to achieve continuous 3D control of the directions of liquid crystal mesogens using a two-step photo-exposure process. In the first step, polarized light sets the orientation in the plane of confining substrates; the second step uses unpolarized light of a prescribed dose to set the out-of-plane orientation. The method enables smoothly varying orientational patterns with sub-micrometer precision. As a demonstration, the setup is used to create gradient-index lenses with parabolic refractive index profiles that remain stable without external electric fields. The lenses' focal length and sensitivity to light polarization are characterized through experimental and numerical methods. The findings pave the way for developing next-generation photonic devices and actuated materials, with potential applications in molecular self-assembly, re-configurable optics, and responsivematter.

Most dynorphin neurons in the zona incerta-perifornical area are active in waking relative to non-rapid-eye movement and rapid-eye movement sleep.

Dynorphin is an endogenous opiate localized in many brain regions and spinal cord, but the activity of dynorphin neurons during sleep is unknown. Dynorphin is an inhibitory neuropeptide that is coreleased with orexin, an excitatory neuropeptide. We used microendoscopy to test the hypothesis that, like orexin, the dynorphin neurons are wake-active. Dynorphin-cre mice (n = 3) were administered rAAV8-Ef1a-Con/Foff 2.0-GCaMP6M into the zona incerta-perifornical area, implanted with a GRIN lens (gradient reflective index), and electrodes to the skull that recorded sleep. One month later, a miniscope imaged calcium fluorescence in dynorphin neurons during multiple bouts of wake, non-rapid-eye movement (NREM), and rapid-eye movement (REM) sleep. Unbiased data analysis identified changes in calcium fluorescence in 64 dynorphin neurons. Most of the dynorphin neurons (72%) had the highest fluorescence during bouts of active and quiet waking compared to NREM or REM sleep; a subset (20%) were REM-max. Our results are consistent with the emerging evidence that the activity of orexin neurons can be classified as wake-max or REM-max. Since the two neuropeptides are coexpressed and coreleased, we suggest that dynorphin-cre-driven calcium sensors could increase understanding of the role of this endogenous opiate in pain and sleep.

Ultra-high-aperture infrared triplet with a GRIN lens: modeling stages of composite gradient-index material and potential possibilities of the optical system

Ultra-high-aperture infrared triplet with a GRIN lens: modeling stages of composite gradient-index material and potential possibilities of the optical system

Design Formulas for Flat Gradient Index Lenses With Planar or Spherical Output Wavefront

Design Formulas for Flat Gradient Index Lenses With Planar or Spherical Output Wavefront

GO Analysis of GRIN Lens Antennas by Combining in a Single ODE, Field and Wavefront-Curvature Transport to the Ray Tracing

GO Analysis of GRIN Lens Antennas by Combining in a Single ODE, Field and Wavefront-Curvature Transport to the Ray Tracing

Parallel compensation of anisoplanatic aberrations in patterned photostimulation for two-photon optogenetics

Two-photon optogenetics becomes an indispensable technique in deciphering neural circuits recently, in which patterned photostimulation is generally adopted due to its low time delay and jitter, as well as its finely sculpting ability in space. However, optical aberrations in light propagation often deteriorates patterned photostimulation, leading to decreased intensity of patterns and thus reduced excitation efficiency. Considering anisoplanatic aberrations at different positions, only correcting aberrations at one position may aggravate aberrations at other positions. Here we propose a parallel aberration compensation based Gerchberg–Saxton (PAC-GS) algorithm for generating multiple holographic extended patterns with anisoplanatic aberrations compensated simultaneously. As an example, we demonstrate that PAC-GS is able to parallelly compensate anisoplanatic aberrations of multiple holographic patterns under gradient index (GRIN) lens, thus effectively improving the intensity of each pattern, promising for two-photon optogenetics in deep biological tissues with GRIN lens.

Distal planar rotary scanner for endoscopic optical coherence tomography.

Optical coherence tomography (OCT) is becoming a more common endoscopic imaging modality for detecting and treating disease given its high resolution and image quality. To use OCT for 3-dimensional imaging of small lumen, embedding an optical scanner at the distal end of an endoscopic probe for circumferential scanning the probing light is a promising way to implement high-quality imaging unachievable with the conventional method of revolving an entire probe. To this end, the present work proposes a hollow and planar micro rotary actuator for its use as an endoscopic distal scanner. A miniaturized design of this ferrofluid-assisted electromagnetic actuator is prototyped to act as a full 360° optical scanner, which is integrated at the tip of a fiber-optic probe together with a gradient-index lens for use with OCT. The scanner is revealed to achieve a notably improved dynamic performance that shows a maximum speed of 6500rpm, representing 325% of the same reported with the preceding design, while staying below the thermal limit for safe in-vivo use. The scanner is demonstrated to perform real-time OCT using human fingers as live tissue samples for the imaging tests. The acquired images display no shadows from the electrical wires to the scanner, given its hollow architecture that allows the probing light to pass through the actuator body, as well as the quality high enough to differentiate the dermis from the epidermis while resolving individual sweat glands, proving the effectiveness of the prototyped scanner design for endoscopic OCT application.

Geometric transformation adaptive optics (GTAO) for volumetric deep brain imaging through gradient-index lenses

The advance of genetic function indicators has enabled the observation of neuronal activities at single-cell resolutions. A major challenge for the applications on mammalian brains is the limited optical access depth. Currently, the method of choice to access deep brain structures is to insert miniature optical components. Among these validated miniature optics, the gradient-index (GRIN) lens has been widely employed for its compactness and simplicity. However, due to strong fourth-order astigmatism, GRIN lenses suffer from a small imaging field of view, which severely limits the measurement throughput and success rate. To overcome these challenges, we developed geometric transformation adaptive optics (GTAO), which enables adaptable achromatic large-volume correction through GRIN lenses. We demonstrate its major advances through in vivo structural and functional imaging of mouse brains. The results suggest that GTAO can serve as a versatile solution to enable large-volume recording of deep brain structures and activities through GRIN lenses.

Structurally embedded gradient index lens for guided wave amplification in polymers

Guided wave inspection is a commonly used technique in structural health monitoring, yet there are challenges associated with ultrasonic inspection of polymeric structures due to high material damping resulting in wave attenuation. In this work, we present a structurally embedded gradient-index phononic crystal (GRIN-PC) lens for elastic wave amplification in polyvinyl chloride (PVC) structures to overcome the attenuation problem in long-range guided wave inspection. The GRIN-PC lens is made up of cylindrical brass stubs of varying heights or diameters embedded in the PVC base structure, providing a hyperbolic secant profile of refractive index distribution transverse to the wave propagation direction. We first demonstrate flexural wave focusing in a PVC plate by implementing the embedded lens design via numerical simulations and experiments. Then, the embedded GRIN-PC lens concept is implemented to PVC pipe for multi-mode wave focusing using a single lens design which is studied through numerical simulations. The proposed GRIN-PC lens design reduces the amplitude decay due to material damping by amplifying the wave energy at the focal regions of the lens. The embedded lens concept developed for polymers can also benefit other applications requiring the transmission of wave energy in structures with high material damping.

A perturbation method for the ray-transfer matrix of the crystalline lens

Analytical expressions for the ray-transfer matrix have been proven useful for the understanding of ray propagation in gradient-index (GRIN) lenses. The determination of an exact analytical expression for the ray-transfer matrix of arbitrary GRIN lenses remains unsolved. We propose an approximation based on the perturbation method with highly accurate results for models of the crystalline lens, which outperforms existing methods.

2D FEM-Based Simulation and Optimization of Concentric Ring GRIN Lens Antennas

2D FEM-Based Simulation and Optimization of Concentric Ring GRIN Lens Antennas

A 3-D Printed Broadband Wide-Angle Multi-Beam Flat GRIN Lens Aided by Multifocal Ray-Path Analyses

A 3-D Printed Broadband Wide-Angle Multi-Beam Flat GRIN Lens Aided by Multifocal Ray-Path Analyses

Graded-Index Lens Based Edge Coupler with Low-Loss, Broad Bandwidth for Efficient Coupling Between Silicon Waveguide and Standard Single-Mode Fiber

Graded-Index Lens Based Edge Coupler with Low-Loss, Broad Bandwidth for Efficient Coupling Between Silicon Waveguide and Standard Single-Mode Fiber

Semi-analytical finite ray-tracing through the quadratic symmetric GRIN lens.

The propagation of light within a gradient index (GRIN) media can be analyzed with the use of differential equations for a given non-homogenous refractive index profile. Numerical methods are often necessary to perform ray-tracing in GRIN media; however, analytical solutions exist for several types of GRIN lenses. In this paper, paraxial and non-paraxial differential equations are derived to calculate the ray path in a GRIN lens. It is shown that the paraxial equation has an analytical solution for a GRIN media with a quadratic profile within the paraxial region. The analytical solution can be obtained by using Legendre polynomials or by the Frobenius method involving a power series. Using the Legendre or Frobenius solution, one can calculate the refractive indices along the ray path. A new recursive relationship is proposed to map the trajectory of light at finite heights. To illustrate the finite ray-tracing method utilizing a non-paraxial differential equation, two lenses (with spherical and elliptical iso-indicial contours) are considered. The lenses' back focal distances, for rays entering the lenses at varying finite heights, are calculated. For each lens, its spherical aberration is estimated. The effective focal length and the shape of the principal surface are also obtained. The accuracy of the results is then compared to the numerical ray-tracing using an optical design software, Zemax OpticStudio. The predicted spherical aberration for the spherical lens differs from numerical ray-tracing by less than λ14 at the marginal zone, while the error for the effective focal length is less than λ100.

Activity of hippocampal CA1 field neurons during aversive memory formation and reactivation in mice <i>in vivo</i>

Activity of hippocampal CA1 field neurons during aversive memory formation and reactivation in mice <i>in vivo</i>

Development of a microelectrode for simultaneous <i>in vivo</i> calcium and electrophysiological recording of hippocampal neuronal activity

Calcium (Ca2+) imaging is a commonly utilized neuroscience technique for in vivo recording of neuronal activity. It involves the optical measurement of calcium concentration using genetically encoded calcium indicators (GECI) [1]. However, the kinetics of changes in the fluorescence of GECI are relatively slow and limited by the biophysics of the calcium binding [2]. In response to single action potentials (APs) in pyramidal neurons, most of the widely used GECI have a fluorescence half-life of approximately 100 ms [3]. As a result, GECI cannot provide complete information about the dynamics of neural ensembles. To address this issue, new variants of GECI, such as jGCaMP7 [3], and jGCaMP8 [4], have been developed, or genetically encoded voltage indicators (GEVI), such as JEDI-2P [5], have been utilized. However, the speed of GECI or GEVI is still lower than that of electrophysiological registration methods. Thus, we have designed a microelectrode that can be utilized with a gradient lens for in vivo calcium imaging with a miniscope. The miniscope is a miniature microscope for single photon epifluorescence Ca2+ imaging, which enables recording of neuronal activity in freely moving laboratory animals, unlike the traditionally used two-photon imaging technique. The miniscope utilizes gradient-index (GRIN) lenses that are implanted directly into the brain of a laboratory animal, instead of a conventional lens. The gradient lens is a transparent cylinder with a diameter of 1.8 mm and a length of 3.8 mm. To facilitate electrophysiological recording, we developed a microelectrode that can be aligned with a GRIN lens. The microelectrode is a three-layer structure consisting of: 1) a polyimide film, 2) conductive copper tracks deposited through thermoforming, and 3) a polyimide film with cutouts for pads. On one side of the microelectrode, there are 12 gold-plated conductive contacts for registering local field potentials, while on the other side, a similar number of conductive tracks are present for connecting to a connector that transmits data to the processing board. The flexible microelectrode is wrapped around a gradient lens and fixed using thermoforming, after which it is implanted in the animal's brain. Using the developed microelectrode, our aim is to perform a comparative analysis of the calcium and electrophysiological activity of hippocampal neurons in freely moving wild-type mice and in a mouse model of Alzheimer's disease. This study will enable the identification of any abnormalities in Alzheimer's disease at the level of neural ensembles and may suggest new treatment approaches or mechanisms for the development of the progressive memory loss pathology associated with this disease. We would like to express our gratitude to Anastasia Viktorovna Bolshakova for her administrative assistance, and to the staff of the Laboratory of Molecular Neurodegeneration for their invaluable help and advices.

Thermally matched chalcogenide glasses with high refractive index contrast for infrared graded‐index lenses

AbstractInfrared graded‐index (GRIN) lenses are desirable for realizing miniaturization and lightweight of infrared imaging systems. Chalcogenide glasses have excellent infrared transparency, good rheological property, and large refractive index range, making them preferred materials for infrared GRIN lenses. In this work, aiming to find thermally matched chalcogenide compositions with high refractive index contrast for preparing GRIN glasses by the stacking diffusion approach, we investigated characteristic temperature, thermal expansion coefficient and refractive index of Ge‐As‐Se and Ge‐As‐Se‐Te glasses, optimized the glass compositions, and evaluated the feasibility of preparing GRIN glass using the optimized chalcogenide glass powders. It is found that Ge20As20Se20Te40 and Ge12As22Se66 glasses have similar softening temperature (247°C vs. 249°C), reasonably difference of thermal expansion coefficient (3.8 ppm/K), and large refractive index contrast (∼.48). The glass powders with composition xGe20As20Se20Te40‐(1‐x) Ge12As22Se66 can be hot‐pressed into glass disks with good transmittance at the same temperature and pressure. Graded refractive index profile is formed near the interface between the layers after the co‐pressed glass is thermally treated. These results demonstrate the prospect of the compositions for preparing infrared GRIN glasses.

Sharp focusing of partially coherent Bessel-correlated beams by a graded-index lens.

The nonparaxial focusing of partially coherent Bessel-correlated beams carrying vortices by a graded-index lens is investigated using the decomposition of the incident field into coherent modes and the quantum mechanical operator method. The influence of the coherence state and the incident beam aperture on tight focusing is analyzed. Our results show that a partially coherent Bessel-correlated beam can be focused into a spot of smaller size than coherent light.

Field curvature reduction in miniaturized high numerical aperture and large field-of-view objective lenses with sub 1 µm lateral resolution.

In this paper the development of a miniaturized endoscopic objective lens for various biophotonics applications is presented. While limiting the mechanical dimensions to 2.2 mm diameter and 13 mm total length, a numerical aperture of 0.7 in water and a field-of-view (FOV) diameter of 282 µm are achieved. To enable multimodal usage a wavelength range of 488 nm to 632 nm was considered. The performed broad design study aimed for field curvature reduction when maintaining the sub 1 µm resolution over a large FOV. Moreover, the usage of GRadient-INdex (GRIN) lenses was investigated. The resolution, field curvature improvement and chromatic performance of the novel device were validated by means of a confocal laser-scanning-microscope.

Symplectic numerical methods in optics and imaging: ray tracing in spherical gradient-index lenses and computer-generated image rendering.

This paper provides an introduction to symplectic numerical integration techniques and examines various optical applications. We first outline the fundamentals of Hamiltonian optics and detail the construction of a symplectic method via the splitting technique. Numerical experiments involving a selection of spherically symmetric gradient-index lenses compare the accuracy of various first-, second-, and fourth-order symplectic methods with equivalent nonsymplectic methods. The best-performing methods are then further tested as part of an image rendering task involving nonlinear ray tracing, comparing the trace time required by each method. Future improvements, recommendations, and uses for symplectic ray tracing are also considered.